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Anonymous
Anonymous asked in 科學及數學數學 · 6 years ago

Curl of a Vector Field (20pts)

a) Let v = [x,y,−z] be the velocity vector of a steady fluid flow. Is the flow

irrotational? Incompressible?

b) With respect to right-handed coordinate, let v = [y+z,z+x,x+y] and

g = xyz , find curl (gv).

1 Answer

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  • 6 years ago
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    a) curl(v)=[0,0,0] , so that the flow v is irrotational

    div(v)=1+1-1 =1 (=/= 0) , the flow v is not incompressible

    b) gv=[xyz(y+z), xyz(z+x), xyz(x+y)]

    curl(gv)=[x^2(z-y), y^2(x-z), z^2(y-x)]

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